THERMAL SCIENCE

International Scientific Journal

Che Haziqah Che Hussin

,

Ahmad Izani Md Ismail

,

Adem Kilicman

,

Amirah Azmi

ANALYTICAL SOLUTIONS OF NONLINEAR KLEIN-GORDON EQUATIONS USING MULTISTEP MODIFIED REDUCED DIFFERENTIAL TRANSFORM METHOD

ABSTRACT
This paper explores the approximate analytical solution of nonlinear Klein-Gordon equations (NKGE) by using Multistep Modified Reduced Differential Transform Method (MMRDTM). Through this proposed strategy, the nonlinear term is substituted by associating Adomian polynomials obtained by utilization of a multistep approach. The NKGE solutions can be obtained with a reduced number of computed terms. In addition, the approximate solutions converge rapidly in a wide time region. Three examples are provided to illustrate the effectiveness of the proposed method to obtain solutions for the NKGE. Graphical results are shown to represent the behavior of the solution so as to demonstrate the validity and accuracy of the MMRDTM.
KEYWORDS
Adomian polynomials, multistep approach, reduced differential transform method, nonlinear Klein-Gordon equations
PAPER SUBMITTED: 2018-10-15
PAPER REVISED: 2018-11-12
PAPER ACCEPTED: 2019-01-16
PUBLISHED ONLINE: 2019-03-09
DOI REFERENCE: https://doi.org/10.2298/TSCI181015045C
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2019, VOLUME 23, ISSUE Supplement 1, PAGES [S317 - S326]
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Analytical solutions of nonlinear Klein-Gordon equations using Multistep Modified Reduced Differential Transform Method

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence